一个二分递归函数的行为不如预期 (R)

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英文:

A bisection recursive function behave not as expected (R)

问题

  1. 我尝试使用递归实现一个简单的二分算法。我以为它有效，但后来想测试它与使用while循环的效率。
  3. 由于某种原因，递归在条件满足之前停止，而while循环（双关语）执行了我期望的操作。
  5. 当尝试将x除以2直到x==0（基本上是计算机的极限）时，x的值停在x = 0.003051758
  7. 代码：
  9. # 尝试比较递归和while方法的二分效率
  10. # 但是递归方法的行为方式不符合预期
  12. # 安装包 "tictoc"
  14. # 方法1：递归
  15. bisect <- function(x,epsilon=0){
  17.   while(x>epsilon){
  18.     cat(x/2,"\n")
  19.     return(bisect(x/2))
  20.   }
  21.   return(x)
  23. } 
  24. # 方法2：while
  25. bisectwhile <- function(x,epsilon=0){
  26.   while(x>epsilon){
  27.     x <- x/2
  28.     print(x)
  29.   }
  30.   return(x)
  31. }
  33. N <- 100
  34. # M1
  35. tictoc::tic()
  36. bisect(N)
  37. tictoc::toc()
  39.     #50 
  40.     #25 
  41.     #.
  42.     #.
  43.     #.
  44.     #0.003051758 
  45.     #[1] 0.003051758
  47. # M2
  48. tictoc::tic()
  49. bisectwhile(N)
  50. tictoc::toc()
英文:

I tried to implement a simple bisection algorithm using recursion. I thought it worked but then i wanted to test its efficiency against using while loop.

For some reason, the recursion stops before the condition is met, while the while loop (pun intended) does what i would expect.

When trying to bisect x/2 untill x==0 (the very limit of the computer basically), its tops at value of x = 0.003051758

Code:

  1. # Trying to compare between recursion and while methods of bisection in terms of efficiency
  2. # However the recursion method behaves in an unexpected way
  4. # install.packages(&quot;tictoc&quot;)
  6. # Mehod 1: recursion
  7. bisect &lt;- function(x,epsilon=0){
  9.   while(x&gt;epsilon){
  10.     cat(x/2,&quot;\n&quot;)
  11.     return(bisect(x/2))
  12.   }
  13.   return(x)
  15. } 
  16. # Method 2: while
  17. bisectwhile &lt;- function(x,epsilon=0){
  18.   while(x&gt;epsilon){
  19.     x &lt;- x/2
  20.     print(x)
  21.   }
  22.   return(x)
  23. }
  25. N &lt;- 100
  26. # M1
  27. tictoc::tic()
  28. bisect(N)
  29. tictoc::toc()
  31.     #50 
  32.     #25 
  33.     #.
  34.     #.
  35.     #.
  36.     #0.003051758 
  37.     #[1] 0.003051758
  39. # M2
  40. tictoc::tic()
  41. bisectwhile(N)
  42. tictoc::toc()

答案1

得分: 1

A loop is faster than recursion here:

  1. bisect_recursive &lt;- function(x) if(x == 0) x else bisect_recursive(x/2)
  2. bisect_loop &lt;- function(x) { while(x != 0) x &lt;- x/2; 0 }

Both of which end up at 0, as you can see:

  1. bisect_recursive(100)
  2. #&gt; x is 100 
  3. #&gt; x is 50 
  4. #&gt; x is 25 
  5. #&gt; x is 12.5 
  6. #&gt; x is 6.25 
  7. #&gt; x is 3.125 
  8. #&gt; x is 1.5625 
  9. #&gt; x is 0.78125 
  10. #&gt; x is 0.390625 
  11. #&gt; x is 0.1953125 
  12. #&gt; x is 0.09765625 
  13. #&gt; x is 0.04882812 
  14. #&gt; x is 0.02441406 
  15. #&gt; x is 0.01220703 
  16. #&gt; x is 0.006103516 
  17. #&gt; x is 0.003051758 
  18. #&gt; x is 0.001525879 
  19. #&gt; x is 0.0007629395 
  20. #&gt; x is 0.0003814697 
  21. #&gt; x is 0.0001907349 
  22. #&gt; x is 9.536743e-05 
  23. #&gt; x is 4.768372e-05 
  24. #&gt; x is 2.384186e-05 
  25. #&gt; x is 1.164153e-05 
  26. #&gt; x is 5.820766e-09 
  27. #&gt; x is 2.910383e-09 
  28. #&gt; x is 1.455192e-09 
  29. #&gt; x is 7.275958e-10 
  30. #&gt; x is 3.637979e-10 
  31. #&gt; x is 1.818989e-10 
  32. #&gt; x is 9.094947e-11 
  33. #&gt; x is 4.547474e-11 
  34. #&gt; x is 2.328306e-11 
  35. #&gt; x is 1.164153e-11 
  36. #&gt; x is 5.820766e-12 
  37. #&gt; x is 2.842171e-12 
  38. #&gt; x is 1.421085e-12 
  39. #&gt; x is 7.105427e-13 
  40. #&gt; x is 3.552714e-13 
  41. #&gt; x is 1.776357e-13 
  42. #&gt; x is 8.881784e-14 
  43. #&gt; x is 4.440892e-14 
  44. #&gt; x is 2.220446e-14 
  45. #&gt; x is 1.110223e-14 
  46. #&gt; x is 5.551115e-15 
  47. #&gt; x is 2.775558e-15 
  48. #&gt; x is 1.387779e-15 
  49. #&gt; x is 6.938894e-16 
  50. #&gt; x is 3.469447e-16 
  51. #&gt; x is 1.734723e-16 
  52. #&gt; x is 8.673617e-17 
  53. #&gt; x is 4.336809e-17 
  54. #&gt; x is 2.168404e-17 
  55. #&gt; x is 1.084202e-17 
  56. #&gt; x is 5.421011e-18 
  57. #&gt; x is 2.710505e-18 
  58. #&gt; x is 1.355253e-18 
  59. #&gt; x is 6.776264e-19 
  60. #&gt; x is 3.388132e-19 
  61. #&gt; x is 1.694066e-19 
  62. #&gt; x is 8.470329e-20 
  63. #&gt; x is 4.235165e-20 
  64. #&gt; x is 2.117582e-20 
  65. #&gt; x is 1.058791e-20 
  66. #&gt; x is 5.293956e-21 
  67. #&gt; x is 2.646978e-21 
  68. #&gt; x is 1.323489e-21 
  69. #&gt; x is 6.617445e-22 
  70. #&gt; x is 3.308722e-22
  72. <details>
  73. <summary>英文:</summary>
  75. A loop is faster than recursion here:
  76. ```r
  77. bisect_recursive &lt;- function(x) if(x == 0) x else bisect_recursive(x/2)
  78. bisect_loop &lt;- function(x) { while(x != 0) x &lt;- x/2; 0 }
  80. N &lt;- 100
  82. microbenchmark::microbenchmark(bisect_recursive(N), bisect_loop(N))
  83. #&gt; Unit: microseconds
  84. #&gt;                 expr   min     lq    mean median    uq    max neval cld
  85. #&gt;  bisect_recursive(N) 916.0 941.95 961.515  953.3 962.8 1334.3   100   b
  86. #&gt;       bisect_loop(N) 491.1 499.20 512.297  508.5 516.6  628.1   100  a

If you want to display all the values, try:

  1. bisect_recursive &lt;- function(x) {
  2.   cat(&quot;x is&quot;, x, &quot;\n&quot;)
  3.   if(x != 0) bisect_recursive(x/2)
  4. }
  6. bisect_loop &lt;- function(x) { 
  7.   while(x != 0) {
  8.     cat(&quot;x is&quot;, x, &quot;\n&quot;)
  9.     x &lt;- x/2 
  10.   }
  11.   cat(&quot;x is&quot;, x, &quot;\n&quot;)
  12. }

Both of which end up at 0, as you can see:

  1. bisect_recursive(100)
  2. #&gt; x is 100 
  3. #&gt; x is 50 
  4. #&gt; x is 25 
  5. #&gt; x is 12.5 
  6. #&gt; x is 6.25 
  7. #&gt; x is 3.125 
  8. #&gt; x is 1.5625 
  9. #&gt; x is 0.78125 
  10. #&gt; x is 0.390625 
  11. #&gt; x is 0.1953125 
  12. #&gt; x is 0.09765625 
  13. #&gt; x is 0.04882812 
  14. #&gt; x is 0.02441406 
  15. #&gt; x is 0.01220703 
  16. #&gt; x is 0.006103516 
  17. #&gt; x is 0.003051758 
  18. #&gt; x is 0.001525879 
  19. #&gt; x is 0.0007629395 
  20. #&gt; x is 0.0003814697 
  21. #&gt; x is 0.0001907349 
  22. #&gt; x is 9.536743e-05 
  23. #&gt; x is 4.768372e-05 
  24. #&gt; x is 2.384186e-05 
  25. #&gt; x is 1.192093e-05 
  26. #&gt; x is 5.960464e-06 
  27. #&gt; x is 2.980232e-06 
  28. #&gt; x is 1.490116e-06 
  29. #&gt; x is 7.450581e-07 
  30. #&gt; x is 3.72529e-07 
  31. #&gt; x is 1.862645e-07 
  32. #&gt; x is 9.313226e-08 
  33. #&gt; x is 4.656613e-08 
  34. #&gt; x is 2.328306e-08 
  35. #&gt; x is 1.164153e-08 
  36. #&gt; x is 5.820766e-09 
  37. #&gt; x is 2.910383e-09 
  38. #&gt; x is 1.455192e-09 
  39. #&gt; x is 7.275958e-10 
  40. #&gt; x is 3.637979e-10 
  41. #&gt; x is 1.818989e-10 
  42. #&gt; x is 9.094947e-11 
  43. #&gt; x is 4.547474e-11 
  44. #&gt; x is 2.273737e-11 
  45. #&gt; x is 1.136868e-11 
  46. #&gt; x is 5.684342e-12 
  47. #&gt; x is 2.842171e-12 
  48. #&gt; x is 1.421085e-12 
  49. #&gt; x is 7.105427e-13 
  50. #&gt; x is 3.552714e-13 
  51. #&gt; x is 1.776357e-13 
  52. #&gt; x is 8.881784e-14 
  53. #&gt; x is 4.440892e-14 
  54. #&gt; x is 2.220446e-14 
  55. #&gt; x is 1.110223e-14 
  56. #&gt; x is 5.551115e-15 
  57. #&gt; x is 2.775558e-15 
  58. #&gt; x is 1.387779e-15 
  59. #&gt; x is 6.938894e-16 
  60. #&gt; x is 3.469447e-16 
  61. #&gt; x is 1.734723e-16 
  62. #&gt; x is 8.673617e-17 
  63. #&gt; x is 4.336809e-17 
  64. #&gt; x is 2.168404e-17 
  65. #&gt; x is 1.084202e-17 
  66. #&gt; x is 5.421011e-18 
  67. #&gt; x is 2.710505e-18 
  68. #&gt; x is 1.355253e-18 
  69. #&gt; x is 6.776264e-19 
  70. #&gt; x is 3.388132e-19 
  71. #&gt; x is 1.694066e-19 
  72. #&gt; x is 8.470329e-20 
  73. #&gt; x is 4.235165e-20 
  74. #&gt; x is 2.117582e-20 
  75. #&gt; x is 1.058791e-20 
  76. #&gt; x is 5.293956e-21 
  77. #&gt; x is 2.646978e-21 
  78. #&gt; x is 1.323489e-21 
  79. #&gt; x is 6.617445e-22 
  80. #&gt; x is 3.308722e-22 
  81. #&gt; x is 1.654361e-22 
  82. #&gt; x is 8.271806e-23 
  83. #&gt; x is 4.135903e-23 
  84. #&gt; x is 2.067952e-23 
  85. #&gt; x is 1.033976e-23 
  86. #&gt; x is 5.169879e-24 
  87. #&gt; x is 2.584939e-24 
  88. #&gt; x is 1.29247e-24 
  89. #&gt; x is 6.462349e-25 
  90. #&gt; x is 3.231174e-25 
  91. #&gt; x is 1.615587e-25 
  92. #&gt; x is 8.077936e-26 
  93. #&gt; x is 4.038968e-26 
  94. #&gt; x is 2.019484e-26 
  95. #&gt; x is 1.009742e-26 
  96. #&gt; x is 5.04871e-27 
  97. #&gt; x is 2.524355e-27 
  98. #&gt; x is 1.262177e-27 
  99. #&gt; x is 6.310887e-28 
  100. #&gt; x is 3.155444e-28 
  101. #&gt; x is 1.577722e-28 
  102. #&gt; x is 7.888609e-29 
  103. #&gt; x is 3.944305e-29 
  104. #&gt; x is 1.972152e-29 
  105. #&gt; x is 9.860761e-30 
  106. #&gt; x is 4.930381e-30 
  107. #&gt; x is 2.46519e-30 
  108. #&gt; x is 1.232595e-30 
  109. #&gt; x is 6.162976e-31 
  110. #&gt; x is 3.081488e-31 
  111. #&gt; x is 1.540744e-31 
  112. #&gt; x is 7.70372e-32 
  113. #&gt; x is 3.85186e-32 
  114. #&gt; x is 1.92593e-32 
  115. #&gt; x is 9.62965e-33 
  116. #&gt; x is 4.814825e-33 
  117. #&gt; x is 2.407412e-33 
  118. #&gt; x is 1.203706e-33 
  119. #&gt; x is 6.018531e-34 
  120. #&gt; x is 3.009266e-34 
  121. #&gt; x is 1.504633e-34 
  122. #&gt; x is 7.523164e-35 
  123. #&gt; x is 3.761582e-35 
  124. #&gt; x is 1.880791e-35 
  125. #&gt; x is 9.403955e-36 
  126. #&gt; x is 4.701977e-36 
  127. #&gt; x is 2.350989e-36 
  128. #&gt; x is 1.175494e-36 
  129. #&gt; x is 5.877472e-37 
  130. #&gt; x is 2.938736e-37 
  131. #&gt; x is 1.469368e-37 
  132. #&gt; x is 7.34684e-38 
  133. #&gt; x is 3.67342e-38 
  134. #&gt; x is 1.83671e-38 
  135. #&gt; x is 9.18355e-39 
  136. #&gt; x is 4.591775e-39 
  137. #&gt; x is 2.295887e-39 
  138. #&gt; x is 1.147944e-39 
  139. #&gt; x is 5.739719e-40 
  140. #&gt; x is 2.869859e-40 
  141. #&gt; x is 1.43493e-40 
  142. #&gt; x is 7.174648e-41 
  143. #&gt; x is 3.587324e-41 
  144. #&gt; x is 1.793662e-41 
  145. #&gt; x is 8.96831e-42 
  146. #&gt; x is 4.484155e-42 
  147. #&gt; x is 2.242078e-42 
  148. #&gt; x is 1.121039e-42 
  149. #&gt; x is 5.605194e-43 
  150. #&gt; x is 2.802597e-43 
  151. #&gt; x is 1.401298e-43 
  152. #&gt; x is 7.006492e-44 
  153. #&gt; x is 3.503246e-44 
  154. #&gt; x is 1.751623e-44 
  155. #&gt; x is 8.758115e-45 
  156. #&gt; x is 4.379058e-45 
  157. #&gt; x is 2.189529e-45 
  158. #&gt; x is 1.094764e-45 
  159. #&gt; x is 5.473822e-46 
  160. #&gt; x is 2.736911e-46 
  161. #&gt; x is 1.368456e-46 
  162. #&gt; x is 6.842278e-47 
  163. #&gt; x is 3.421139e-47 
  164. #&gt; x is 1.710569e-47 
  165. #&gt; x is 8.552847e-48 
  166. #&gt; x is 4.276424e-48 
  167. #&gt; x is 2.138212e-48 
  168. #&gt; x is 1.069106e-48 
  169. #&gt; x is 5.345529e-49 
  170. #&gt; x is 2.672765e-49 
  171. #&gt; x is 1.336382e-49 
  172. #&gt; x is 6.681912e-50 
  173. #&gt; x is 3.340956e-50 
  174. #&gt; x is 1.670478e-50 
  175. #&gt; x is 8.35239e-51 
  176. #&gt; x is 4.176195e-51 
  177. #&gt; x is 2.088097e-51 
  178. #&gt; x is 1.044049e-51 
  179. #&gt; x is 5.220244e-52 
  180. #&gt; x is 2.610122e-52 
  181. #&gt; x is 1.305061e-52 
  182. #&gt; x is 6.525304e-53 
  183. #&gt; x is 3.262652e-53 
  184. #&gt; x is 1.631326e-53 
  185. #&gt; x is 8.156631e-54 
  186. #&gt; x is 4.078315e-54 
  187. #&gt; x is 2.039158e-54 
  188. #&gt; x is 1.019579e-54 
  189. #&gt; x is 5.097894e-55 
  190. #&gt; x is 2.548947e-55 
  191. #&gt; x is 1.274474e-55 
  192. #&gt; x is 6.372368e-56 
  193. #&gt; x is 3.186184e-56 
  194. #&gt; x is 1.593092e-56 
  195. #&gt; x is 7.96546e-57 
  196. #&gt; x is 3.98273e-57 
  197. #&gt; x is 1.991365e-57 
  198. #&gt; x is 9.956824e-58 
  199. #&gt; x is 4.978412e-58 
  200. #&gt; x is 2.489206e-58 
  201. #&gt; x is 1.244603e-58 
  202. #&gt; x is 6.223015e-59 
  203. #&gt; x is 3.111508e-59 
  204. #&gt; x is 1.555754e-59 
  205. #&gt; x is 7.778769e-60 
  206. #&gt; x is 3.889385e-60 
  207. #&gt; x is 1.944692e-60 
  208. #&gt; x is 9.723461e-61 
  209. #&gt; x is 4.861731e-61 
  210. #&gt; x is 2.430865e-61 
  211. #&gt; x is 1.215433e-61 
  212. #&gt; x is 6.077163e-62 
  213. #&gt; x is 3.038582e-62 
  214. #&gt; x is 1.519291e-62 
  215. #&gt; x is 7.596454e-63 
  216. #&gt; x is 3.798227e-63 
  217. #&gt; x is 1.899114e-63 
  218. #&gt; x is 9.495568e-64 
  219. #&gt; x is 4.747784e-64 
  220. #&gt; x is 2.373892e-64 
  221. #&gt; x is 1.186946e-64 
  222. #&gt; x is 5.93473e-65 
  223. #&gt; x is 2.967365e-65 
  224. #&gt; x is 1.483682e-65 
  225. #&gt; x is 7.418412e-66 
  226. #&gt; x is 3.709206e-66 
  227. #&gt; x is 1.854603e-66 
  228. #&gt; x is 9.273015e-67 
  229. #&gt; x is 4.636508e-67 
  230. #&gt; x is 2.318254e-67 
  231. #&gt; x is 1.159127e-67 
  232. #&gt; x is 5.795635e-68 
  233. #&gt; x is 2.897817e-68 
  234. #&gt; x is 1.448909e-68 
  235. #&gt; x is 7.244543e-69 
  236. #&gt; x is 3.622272e-69 
  237. #&gt; x is 1.811136e-69 
  238. #&gt; x is 9.055679e-70 
  239. #&gt; x is 4.52784e-70 
  240. #&gt; x is 2.26392e-70 
  241. #&gt; x is 1.13196e-70 
  242. #&gt; x is 5.659799e-71 
  243. #&gt; x is 2.8299e-71 
  244. #&gt; x is 1.41495e-71 
  245. #&gt; x is 7.074749e-72 
  246. #&gt; x is 3.537375e-72 
  247. #&gt; x is 1.768687e-72 
  248. #&gt; x is 8.843437e-73 
  249. #&gt; x is 4.421718e-73 
  250. #&gt; x is 2.210859e-73 
  251. #&gt; x is 1.10543e-73 
  252. #&gt; x is 5.527148e-74 
  253. #&gt; x is 2.763574e-74 
  254. #&gt; x is 1.381787e-74 
  255. #&gt; x is 6.908935e-75 
  256. #&gt; x is 3.454467e-75 
  257. #&gt; x is 1.727234e-75 
  258. #&gt; x is 8.636169e-76 
  259. #&gt; x is 4.318084e-76 
  260. #&gt; x is 2.159042e-76 
  261. #&gt; x is 1.079521e-76 
  262. #&gt; x is 5.397605e-77 
  263. #&gt; x is 2.698803e-77 
  264. #&gt; x is 1.349401e-77 
  265. #&gt; x is 6.747007e-78 
  266. #&gt; x is 3.373503e-78 
  267. #&gt; x is 1.686752e-78 
  268. #&gt; x is 8.433758e-79 
  269. #&gt; x is 4.216879e-79 
  270. #&gt; x is 2.10844e-79 
  271. #&gt; x is 1.05422e-79 
  272. #&gt; x is 5.271099e-80 
  273. #&gt; x is 2.635549e-80 
  274. #&gt; x is 1.317775e-80 
  275. #&gt; x is 6.588874e-81 
  276. #&gt; x is 3.294437e-81 
  277. #&gt; x is 1.647218e-81 
  278. #&gt; x is 8.236092e-82 
  279. #&gt; x is 4.118046e-82 
  280. #&gt; x is 2.059023e-82 
  281. #&gt; x is 1.029512e-82 
  282. #&gt; x is 5.147558e-83 
  283. #&gt; x is 2.573779e-83 
  284. #&gt; x is 1.286889e-83 
  285. #&gt; x is 6.434447e-84 
  286. #&gt; x is 3.217223e-84 
  287. #&gt; x is 1.608612e-84 
  288. #&gt; x is 8.043059e-85 
  289. #&gt; x is 4.021529e-85 
  290. #&gt; x is 2.010765e-85 
  291. #&gt; x is 1.005382e-85 
  292. #&gt; x is 5.026912e-86 
  293. #&gt; x is 2.513456e-86 
  294. #&gt; x is 1.256728e-86 
  295. #&gt; x is 6.28364e-87 
  296. #&gt; x is 3.14182e-87 
  297. #&gt; x is 1.57091e-87 
  298. #&gt; x is 7.85455e-88 
  299. #&gt; x is 3.927275e-88 
  300. #&gt; x is 1.963637e-88 
  301. #&gt; x is 9.818187e-89 
  302. #&gt; x is 4.909093e-89 
  303. #&gt; x is 2.454547e-89 
  304. #&gt; x is 1.227273e-89 
  305. #&gt; x is 6.136367e-90 
  306. #&gt; x is 3.068183e-90 
  307. #&gt; x is 1.534092e-90 
  308. #&gt; x is 7.670459e-91 
  309. #&gt; x is 3.835229e-91 
  310. #&gt; x is 1.917615e-91 
  311. #&gt; x is 9.588073e-92 
  312. #&gt; x is 4.794037e-92 
  313. #&gt; x is 2.397018e-92 
  314. #&gt; x is 1.198509e-92 
  315. #&gt; x is 5.992546e-93 
  316. #&gt; x is 2.996273e-93 
  317. #&gt; x is 1.498136e-93 
  318. #&gt; x is 7.490682e-94 
  319. #&gt; x is 3.745341e-94 
  320. #&gt; x is 1.872671e-94 
  321. #&gt; x is 9.363353e-95 
  322. #&gt; x is 4.681676e-95 
  323. #&gt; x is 2.340838e-95 
  324. #&gt; x is 1.170419e-95 
  325. #&gt; x is 5.852095e-96 
  326. #&gt; x is 2.926048e-96 
  327. #&gt; x is 1.463024e-96 
  328. #&gt; x is 7.315119e-97 
  329. #&gt; x is 3.65756e-97 
  330. #&gt; x is 1.82878e-97 
  331. #&gt; x is 9.143899e-98 
  332. #&gt; x is 4.57195e-98 
  333. #&gt; x is 2.285975e-98 
  334. #&gt; x is 1.142987e-98 
  335. #&gt; x is 5.714937e-99 
  336. #&gt; x is 2.857468e-99 
  337. #&gt; x is 1.428734e-99 
  338. #&gt; x is 7.143671e-100 
  339. #&gt; x is 3.571836e-100 
  340. #&gt; x is 1.785918e-100 
  341. #&gt; x is 8.929589e-101 
  342. #&gt; x is 4.464794e-101 
  343. #&gt; x is 2.232397e-101 
  344. #&gt; x is 1.116199e-101 
  345. #&gt; x is 5.580993e-102 
  346. #&gt; x is 2.790497e-102 
  347. #&gt; x is 1.395248e-102 
  348. #&gt; x is 6.976241e-103 
  349. #&gt; x is 3.488121e-103 
  350. #&gt; x is 1.74406e-103 
  351. #&gt; x is 8.720302e-104 
  352. #&gt; x is 4.360151e-104 
  353. #&gt; x is 2.180075e-104 
  354. #&gt; x is 1.090038e-104 
  355. #&gt; x is 5.450189e-105 
  356. #&gt; x is 2.725094e-105 
  357. #&gt; x is 1.362547e-105 
  358. #&gt; x is 6.812736e-106 
  359. #&gt; x is 3.406368e-106 
  360. #&gt; x is 1.703184e-106 
  361. #&gt; x is 8.51592e-107 
  362. #&gt; x is 4.25796e-107 
  363. #&gt; x is 2.12898e-107 
  364. #&gt; x is 1.06449e-107 
  365. #&gt; x is 5.32245e-108 
  366. #&gt; x is 2.661225e-108 
  367. #&gt; x is 1.330612e-108 
  368. #&gt; x is 6.653062e-109 
  369. #&gt; x is 3.326531e-109 
  370. #&gt; x is 1.663266e-109 
  371. #&gt; x is 8.316328e-110 
  372. #&gt; x is 4.158164e-110 
  373. #&gt; x is 2.079082e-110 
  374. #&gt; x is 1.039541e-110 
  375. #&gt; x is 5.197705e-111 
  376. #&gt; x is 2.598852e-111 
  377. #&gt; x is 1.299426e-111 
  378. #&gt; x is 6.497131e-112 
  379. #&gt; x is 3.248566e-112 
  380. #&gt; x is 1.624283e-112 
  381. #&gt; x is 8.121414e-113 
  382. #&gt; x is 4.060707e-113 
  383. #&gt; x is 2.030353e-113 
  384. #&gt; x is 1.015177e-113 
  385. #&gt; x is 5.075884e-114 
  386. #&gt; x is 2.537942e-114 
  387. #&gt; x is 1.268971e-114 
  388. #&gt; x is 6.344855e-115 
  389. #&gt; x is 3.172427e-115 
  390. #&gt; x is 1.586214e-115 
  391. #&gt; x is 7.931068e-116 
  392. #&gt; x is 3.965534e-116 
  393. #&gt; x is 1.982767e-116 
  394. #&gt; x is 9.913835e-117 
  395. #&gt; x is 4.956918e-117 
  396. #&gt; x is 2.478459e-117 
  397. #&gt; x is 1.239229e-117 
  398. #&gt; x is 6.196147e-118 
  399. #&gt; x is 3.098074e-118 
  400. #&gt; x is 1.549037e-118 
  401. #&gt; x is 7.745184e-119 
  402. #&gt; x is 3.872592e-119 
  403. #&gt; x is 1.936296e-119 
  404. #&gt; x is 9.68148e-120 
  405. #&gt; x is 4.84074e-120 
  406. #&gt; x is 2.42037e-120 
  407. #&gt; x is 1.210185e-120 
  408. #&gt; x is 6.050925e-121 
  409. #&gt; x is 3.025462e-121 
  410. #&gt; x is 1.512731e-121 
  411. #&gt; x is 7.563656e-122 
  412. #&gt; x is 3.781828e-122 
  413. #&gt; x is 1.890914e-122 
  414. #&gt; x is 9.45457e-123 
  415. #&gt; x is 4.727285e-123 
  416. #&gt; x is 2.363643e-123 
  417. #&gt; x is 1.181821e-123 
  418. #&gt; x is 5.909106e-124 
  419. #&gt; x is 2.954553e-124 
  420. #&gt; x is 1.477277e-124 
  421. #&gt; x is 7.386383e-125 
  422. #&gt; x is 3.693191e-125 
  423. #&gt; x is 1.846596e-125 
  424. #&gt; x is 9.232979e-126 
  425. #&gt; x is 4.616489e-126 
  426. #&gt; x is 2.308245e-126 
  427. #&gt; x is 1.154122e-126 
  428. #&gt; x is 5.770612e-127 
  429. #&gt; x is 2.885306e-127 
  430. #&gt; x is 1.442653e-127 
  431. #&gt; x is 7.213265e-128 
  432. #&gt; x is 3.606632e-128 
  433. #&gt; x is 1.803316e-128 
  434. #&gt; x is 9.016581e-129 
  435. #&gt; x is 4.50829e-129 
  436. #&gt; x is 2.254145e-129 
  437. #&gt; x is 1.127073e-129 
  438. #&gt; x is 5.635363e-130 
  439. #&gt; x is 2.817681e-130 
  440. #&gt; x is 1.408841e-130 
  441. #&gt; x is 7.044204e-131 
  442. #&gt; x is 3.522102e-131 
  443. #&gt; x is 1.761051e-131 
  444. #&gt; x is 8.805255e-132 
  445. #&gt; x is 4.402627e-132 
  446. #&gt; x is 2.201314e-132 
  447. #&gt; x is 1.100657e-132 
  448. #&gt; x is 5.503284e-133 
  449. #&gt; x is 2.751642e-133 
  450. #&gt; x is 1.375821e-133 
  451. #&gt; x is 6.879105e-134 
  452. #&gt; x is 3.439553e-134 
  453. #&gt; x is 1.719776e-134 
  454. #&gt; x is 8.598881e-135 
  455. #&gt; x is 4.299441e-135 
  456. #&gt; x is 2.14972e-135 
  457. #&gt; x is 1.07486e-135 
  458. #&gt; x is 5.374301e-136 
  459. #&gt; x is 2.68715e-136 
  460. #&gt; x is 1.343575e-136 
  461. #&gt; x is 6.717876e-137 
  462. #&gt; x is 3.358938e-137 
  463. #&gt; x is 1.679469e-137 
  464. #&gt; x is 8.397345e-138 
  465. #&gt; x is 4.198673e-138 
  466. #&gt; x is 2.099336e-138 
  467. #&gt; x is 1.049668e-138 
  468. #&gt; x is 5.248341e-139 
  469. #&gt; x is 2.62417e-139 
  470. #&gt; x is 1.312085e-139 
  471. #&gt; x is 6.560426e-140 
  472. #&gt; x is 3.280213e-140 
  473. #&gt; x is 1.640106e-140 
  474. #&gt; x is 8.200532e-141 
  475. #&gt; x is 4.100266e-141 
  476. #&gt; x is 2.050133e-141 
  477. #&gt; x is 1.025067e-141 
  478. #&gt; x is 5.125333e-142 
  479. #&gt; x is 2.562666e-142 
  480. #&gt; x is 1.281333e-142 
  481. #&gt; x is 6.406666e-143 
  482. #&gt; x is 3.203333e-143 
  483. #&gt; x is 1.601666e-143 
  484. #&gt; x is 8.008332e-144 
  485. #&gt; x is 4.004166e-144 
  486. #&gt; x is 2.002083e-144 
  487. #&gt; x is 1.001042e-144 
  488. #&gt; x is 5.005208e-145 
  489. #&gt; x is 2.502604e-145 
  490. #&gt; x is 1.251302e-145 
  491. #&gt; x is 6.25651e-146 
  492. #&gt; x is 3.128255e-146 
  493. #&gt; x is 1.564127e-146 
  494. #&gt; x is 7.820637e-147 
  495. #&gt; x is 3.910319e-147 
  496. #&gt; x is 1.955159e-147 
  497. #&gt; x is 9.775796e-148 
  498. #&gt; x is 4.887898e-148 
  499. #&gt; x is 2.443949e-148 
  500. #&gt; x is 1.221975e-148 
  501. #&gt; x is 6.109873e-149 
  502. #&gt; x is 3.054936e-149 
  503. #&gt; x is 1.527468e-149 
  504. #&gt; x is 7.637341e-150 
  505. #&gt; x is 3.81867e-150 
  506. #&gt; x is 1.909335e-150 
  507. #&gt; x is 9.546676e-151 
  508. #&gt; x is 4.773338e-151 
  509. #&gt; x is 2.386669e-151 
  510. #&gt; x is 1.193335e-151 
  511. #&gt; x is 5.966673e-152 
  512. #&gt; x is 2.983336e-152 
  513. #&gt; x is 1.491668e-152 
  514. #&gt; x is 7.458341e-153 
  515. #&gt; x is 3.72917e-153 
  516. #&gt; x is 1.864585e-153 
  517. #&gt; x is 9.322926e-154 
  518. #&gt; x is 4.661463e-154 
  519. #&gt; x is 2.330731e-154 
  520. #&gt; x is 1.165366e-154 
  521. #&gt; x is 5.826829e-155 
  522. #&gt; x is 2.913414e-155 
  523. #&gt; x is 1.456707e-155 
  524. #&gt; x is 7.283536e-156 
  525. #&gt; x is 3.641768e-156 
  526. #&gt; x is 1.820884e-156 
  527. #&gt; x is 9.10442e-157 
  528. #&gt; x is 4.55221e-157 
  529. #&gt; x is 2.276105e-157 
  530. #&gt; x is 1.138052e-157 
  531. #&gt; x is 5.690262e-158 
  532. #&gt; x is 2.845131e-158 
  533. #&gt; x is 1.422566e-158 
  534. #&gt; x is 7.112828e-159 
  535. #&gt; x is 3.556414e-159 
  536. #&gt; x is 1.778207e-159 
  537. #&gt; x is 8.891035e-160 
  538. #&gt; x is 4.445517e-160 
  539. #&gt; x is 2.222759e-160 
  540. #&gt; x is 1.111379e-160 
  541. #&gt; x is 5.556897e-161 
  542. #&gt; x is 2.778448e-161 
  543. #&gt; x is 1.389224e-161 
  544. #&gt; x is 6.946121e-162 
  545. #&gt; x is 3.473061e-162 
  546. #&gt; x is 1.73653e-162 
  547. #&gt; x is 8.682651e-163 
  548. #&gt; x is 4.341326e-163 
  549. #&gt; x is 2.170663e-163 
  550. #&gt; x is 1.085331e-163 
  551. #&gt; x is 5.426657e-164 
  552. #&gt; x is 2.713329e-164 
  553. #&gt; x is 1.356664e-164 
  554. #&gt; x is 6.783321e-165 
  555. #&gt; x is 3.391661e-165 
  556. #&gt; x is 1.69583e-165 
  557. #&gt; x is 8.479152e-166 
  558. #&gt; x is 4.239576e-166 
  559. #&gt; x is 2.119788e-166 
  560. #&gt; x is 1.059894e-166 
  561. #&gt; x is 5.29947e-167 
  562. #&gt; x is 2.649735e-167 
  563. #&gt; x is 1.324867e-167 
  564. #&gt; x is 6.624337e-168 
  565. #&gt; x is 3.312169e-168 
  566. #&gt; x is 1.656084e-168 
  567. #&gt; x is 8.280422e-169 
  568. #&gt; x is 4.140211e-169 
  569. #&gt; x is 2.070105e-169 
  570. #&gt; x is 1.035053e-169 
  571. #&gt; x is 5.175264e-170 
  572. #&gt; x is 2.587632e-170 
  573. #&gt; x is 1.293816e-170 
  574. #&gt; x is 6.469079e-171 
  575. #&gt; x is 3.23454e-171 
  576. #&gt; x is 1.61727e-171 
  577. #&gt; x is 8.086349e-172 
  578. #&gt; x is 4.043175e-172 
  579. #&gt; x is 2.021587e-172 
  580. #&gt; x is 1.010794e-172 
  581. #&gt; x is 5.053968e-173 
  582. #&gt; x is 2.526984e-173 
  583. #&gt; x is 1.263492e-173 
  584. #&gt; x is 6.31746e-174 
  585. #&gt; x is 3.15873e-174 
  586. #&gt; x is 1.579365e-174 
  587. #&gt; x is 7.896825e-175 
  588. #&gt; x is 3.948413e-175 
  589. #&gt; x is 1.974206e-175 
  590. #&gt; x is 9.871032e-176 
  591. #&gt; x is 4.935516e-176 
  592. #&gt; x is 2.467758e-176 
  593. #&gt; x is 1.233879e-176 
  594. #&gt; x is 6.169395e-177 
  595. #&gt; x is 3.084697e-177 
  596. #&gt; x is 1.542349e-177 
  597. #&gt; x is 7.711744e-178 
  598. #&gt; x is 3.855872e-178 
  599. #&gt; x is 1.927936e-178 
  600. #&gt; x is 9.639679e-179 
  601. #&gt; x is 4.81984e-179 
  602. #&gt; x is 2.40992e-179 
  603. #&gt; x is 1.20496e-179 
  604. #&gt; x is 6.0248e-180 
  605. #&gt; x is 3.0124e-180 
  606. #&gt; x is 1.5062e-180 
  607. #&gt; x is 7.531e-181 
  608. #&gt; x is 3.7655e-181 
  609. #&gt; x is 1.88275e-181 
  610. #&gt; x is 9.413749e-182 
  611. #&gt; x is 4.706875e-182 
  612. #&gt; x is 2.353437e-182 
  613. #&gt; x is 1.176719e-182 
  614. #&gt; x is 5.883593e-183 
  615. #&gt; x is 2.941797e-183 
  616. #&gt; x is 1.470898e-183 
  617. #&gt; x is 7.354492e-184 
  618. #&gt; x is 3.677246e-184 
  619. #&gt; x is 1.838623e-184 
  620. #&gt; x is 9.193115e-185 
  621. #&gt; x is 4.596557e-185 
  622. #&gt; x is 2.298279e-185 
  623. #&gt; x is 1.149139e-185 
  624. #&gt; x is 5.745697e-186 
  625. #&gt; x is 2.872848e-186 
  626. #&gt; x is 1.436424e-186 
  627. #&gt; x is 7.182121e-187 
  628. #&gt; x is 3.59106e-187 
  629. #&gt; x is 1.79553e-187 
  630. #&gt; x is 8.977651e-188 
  631. #&gt; x is 4.488826e-188 
  632. #&gt; x is 2.244413e-188 
  633. #&gt; x is 1.122206e-188 
  634. #&gt; x is 5.611032e-189 
  635. #&gt; x is 2.805516e-189 
  636. #&gt; x is 1.402758e-189 
  637. #&gt; x is 7.01379e-190 
  638. #&gt; x is 3.506895e-190 
  639. #&gt; x is 1.753447e-190 
  640. #&gt; x is 8.767237e-191 
  641. #&gt; x is 4.383619e-191 
  642. #&gt; x is 2.191809e-191 
  643. #&gt; x is 1.095905e-191 
  644. #&gt; x is 5.479523e-192 
  645. #&gt; x is 2.739762e-192 
  646. #&gt; x is 1.369881e-192 
  647. #&gt; x is 6.849404e-193 
  648. #&gt; x is 3.424702e-193 
  649. #&gt; x is 1.712351e-193 
  650. #&gt; x is 8.561755e-194 
  651. #&gt; x is 4.280878e-194 
  652. #&gt; x is 2.140439e-194 
  653. #&gt; x is 1.070219e-194 
  654. #&gt; x is 5.351097e-195 
  655. #&gt; x is 2.675549e-195 
  656. #&gt; x is 1.337774e-195 
  657. #&gt; x is 6.688871e-196 
  658. #&gt; x is 3.344436e-196 
  659. #&gt; x is 1.672218e-196 
  660. #&gt; x is 8.361089e-197 
  661. #&gt; x is 4.180545e-197 
  662. #&gt; x is 2.090272e-197 
  663. #&gt; x is 1.045136e-197 
  664. #&gt; x is 5.225681e-198 
  665. #&gt; x is 2.61284e-198 
  666. #&gt; x is 1.30642e-198 
  667. #&gt; x is 6.532101e-199 
  668. #&gt; x is 3.26605e-199 
  669. #&gt; x is 1.633025e-199 
  670. #&gt; x is 8.165126e-200 
  671. #&gt; x is 4.082563e-200 
  672. #&gt; x is 2.041282e-200 
  673. #&gt; x is 1.020641e-200 
  674. #&gt; x is 5.103204e-201 
  675. #&gt; x is 2.551602e-201 
  676. #&gt; x is 1.275801e-201 
  677. #&gt; x is 6.379005e-202 
  678. #&gt; x is 3.189502e-202 
  679. #&gt; x is 1.594751e-202 
  680. #&gt; x is 7.973756e-203 
  681. #&gt; x is 3.986878e-203 
  682. #&gt; x is 1.993439e-203 
  683. #&gt; x is 9.967195e-204 
  684. #&gt; x is 4.983597e-204 
  685. #&gt; x is 2.491799e-204 
  686. #&gt; x is 1.245899e-204 
  687. #&gt; x is 6.229497e-205 
  688. #&gt; x is 3.114748e-205 
  689. #&gt; x is 1.557374e-205 
  690. #&gt; x is 7.786871e-206 
  691. #&gt; x is 3.893436e-206 
  692. #&gt; x is 1.946718e-206 
  693. #&gt; x is 9.733589e-207 
  694. #&gt; x is 4.866794e-207 
  695. #&gt; x is 2.433397e-207 
  696. #&gt; x is 1.216699e-207 
  697. #&gt; x is 6.083493e-208 
  698. #&gt; x is 3.041747e-208 
  699. #&gt; x is 1.520873e-208 
  700. #&gt; x is 7.604366e-209 
  701. #&gt; x is 3.802183e-209 
  702. #&gt; x is 1.901092e-209 
  703. #&gt; x is 9.505458e-210 
  704. #&gt; x is 4.752729e-210 
  705. #&gt; x is 2.376364e-210 
  706. #&gt; x is 1.188182e-210 
  707. #&gt; x is 5.940911e-211 
  708. #&gt; x is 2.970456e-211 
  709. #&gt; x is 1.485228e-211 
  710. #&gt; x is 7.426139e-212 
  711. #&gt; x is 3.713069e-212 
  712. #&gt; x is 1.856535e-212 
  713. #&gt; x is 9.282674e-213 
  714. #&gt; x is 4.641337e-213 
  715. #&gt; x is 2.320668e-213 
  716. #&gt; x is 1.160334e-213 
  717. #&gt; x is 5.801671e-214 
  718. #&gt; x is 2.900836e-214 
  719. #&gt; x is 1.450418e-214 
  720. #&gt; x is 7.252089e-215 
  721. #&gt; x is 3.626044e-215 
  722. #&gt; x is 1.813022e-215 
  723. #&gt; x is 9.065111e-216 
  724. #&gt; x is 4.532555e-216 
  725. #&gt; x is 2.266278e-216 
  726. #&gt; x is 1.133139e-216 
  727. #&gt; x is 5.665694e-217 
  728. #&gt; x is 2.832847e-217 
  729. #&gt; x is 1.416424e-217 
  730. #&gt; x is 7.082118e-218 
  731. #&gt; x is 3.541059e-218 
  732. #&gt; x is 1.770529e-218 
  733. #&gt; x is 8.852647e-219 
  734. #&gt; x is 4.426324e-219 
  735. #&gt; x is 2.213162e-219 
  736. #&gt; x is 1.106581e-219 
  737. #&gt; x is 5.532905e-220 
  738. #&gt; x is 2.766452e-220 
  739. #&gt; x is 1.383226e-220 
  740. #&gt; x is 6.916131e-221 
  741. #&gt; x is 3.458065e-221 
  742. #&gt; x is 1.729033e-221 
  743. #&gt; x is 8.645164e-222 
  744. #&gt; x is 4.322582e-222 
  745. #&gt; x is 2.161291e-222 
  746. #&gt; x is 1.080645e-222 
  747. #&gt; x is 5.403227e-223 
  748. #&gt; x is 2.701614e-223 
  749. #&gt; x is 1.350807e-223 
  750. #&gt; x is 6.754034e-224 
  751. #&gt; x is 3.377017e-224 
  752. #&gt; x is 1.688509e-224 
  753. #&gt; x is 8.442543e-225 
  754. #&gt; x is 4.221271e-225 
  755. #&gt; x is 2.110636e-225 
  756. #&gt; x is 1.055318e-225 
  757. #&gt; x is 5.276589e-226 
  758. #&gt; x is 2.638295e-226 
  759. #&gt; x is 1.319147e-226 
  760. #&gt; x is 6.595736e-227 
  761. #&gt; x is 3.297868e-227 
  762. #&gt; x is 1.648934e-227 
  763. #&gt; x is 8.24467e-228 
  764. #&gt; x is 4.122335e-228 
  765. #&gt; x is 2.061168e-228 
  766. #&gt; x is 1.030584e-228 
  767. #&gt; x is 5.152919e-229 
  768. #&gt; x is 2.57646e-229 
  769. #&gt; x is 1.28823e-229 
  770. #&gt; x is 6.441149e-230 
  771. #&gt; x is 3.220574e-230 
  772. #&gt; x is 1.610287e-230 
  773. #&gt; x is 8.051436e-231 
  774. #&gt; x is 4.025718e-231 
  775. #&gt; x is 2.012859e-231 
  776. #&gt; x is 1.006429e-231 
  777. #&gt; x is 5.032147e-232 
  778. #&gt; x is 2.516074e-232 
  779. #&gt; x is 1.258037e-232 
  780. #&gt; x is 6.290184e-233 
  781. #&gt; x is 3.145092e-233 
  782. #&gt; x is 1.572546e-233 
  783. #&gt; x is 7.86273e-234 
  784. #&gt; x is 3.931365e-234 
  785. #&gt; x is 1.965683e-234 
  786. #&gt; x is 9.828413e-235 
  787. #&gt; x is 4.914207e-235 
  788. #&gt; x is 2.457103e-235 
  789. #&gt; x is 1.228552e-235 
  790. #&gt; x is 6.142758e-236 
  791. #&gt; x is 3.071379e-236 
  792. #&gt; x is 1.53569e-236 
  793. #&gt; x is 7.678448e-237 
  794. #&gt; x is 3.839224e-237 
  795. #&gt; x is 1.919612e-237 
  796. #&gt; x is 9.59806e-238 
  797. #&gt; x is 4.79903e-238 
  798. #&gt; x is 2.399515e-238 
  799. #&gt; x is 1.199757e-238 
  800. #&gt; x is 5.998787e-239 
  801. #&gt; x is 2.999394e-239 
  802. #&gt; x is 1.499697e-239 
  803. #&gt; x is 7.498484e-240 
  804. #&gt; x is 3.749242e-240 
  805. #&gt; x is 1.874621e-240 
  806. #&gt; x is 9.373105e-241 
  807. #&gt; x is 4.686553e-241 
  808. #&gt; x is 2.343276e-241 
  809. #&gt; x is 1.171638e-241 
  810. #&gt; x is 5.858191e-242 
  811. #&gt; x is 2.929095e-242 
  812. #&gt; x is 1.464548e-242 
  813. #&gt; x is 7.322738e-243 
  814. #&gt; x is 3.661369e-243 
  815. #&gt; x is 1.830685e-243 
  816. #&gt; x is 9.153423e-244 
  817. #&gt; x is 4.576711e-244 
  818. #&gt; x is 2.288356e-244 
  819. #&gt; x is 1.144178e-244 
  820. #&gt; x is 5.720889e-245 
  821. #&gt; x is 2.860445e-245 
  822. #&gt; x is 1.430222e-245 
  823. #&gt; x is 7.151112e-246 
  824. #&gt; x is 3.575556e-246 
  825. #&gt; x is 1.787778e-246 
  826. #&gt; x is 8.93889e-247 
  827. #&gt; x is 4.469445e-247 
  828. #&gt; x is 2.234722e-247 
  829. #&gt; x is 1.117361e-247 
  830. #&gt; x is 5.586806e-248 
  831. #&gt; x is 2.793403e-248 
  832. #&gt; x is 1.396701e-248 
  833. #&gt; x is 6.983507e-249 
  834. #&gt; x is 3.491754e-249 
  835. #&gt; x is 1.745877e-249 
  836. #&gt; x is 8.729384e-250 
  837. #&gt; x is 4.364692e-250 
  838. #&gt; x is 2.182346e-250 
  839. #&gt; x is 1.091173e-250 
  840. #&gt; x is 5.455865e-251 
  841. #&gt; x is 2.727933e-251 
  842. #&gt; x is 1.363966e-251 
  843. #&gt; x is 6.819832e-252 
  844. #&gt; x is 3.409916e-252 
  845. #&gt; x is 1.704958e-252 
  846. #&gt; x is 8.524789e-253 
  847. #&gt; x is 4.262395e-253 
  848. #&gt; x is 2.131197e-253 
  849. #&gt; x is 1.065599e-253 
  850. #&gt; x is 5.327993e-254 
  851. #&gt; x is 2.663997e-254 
  852. #&gt; x is 1.331998e-254 
  853. #&gt; x is 6.659992e-255 
  854. #&gt; x is 3.329996e-255 
  855. #&gt; x is 1.664998e-255 
  856. #&gt; x is 8.32499e-256 
  857. #&gt; x is 4.162495e-256 
  858. #&gt; x is 2.081247e-256 
  859. #&gt; x is 1.040624e-256 
  860. #&gt; x is 5.203119e-257 
  861. #&gt; x is 2.601559e-257 
  862. #&gt; x is 1.30078e-257 
  863. #&gt; x is 6.503898e-258 
  864. #&gt; x is 3.251949e-258 
  865. #&gt; x is 1.625975e-258 
  866. #&gt; x is 8.129873e-259 
  867. #&gt; x is 4.064936e-259 
  868. #&gt; x is 2.032468e-259 
  869. #&gt; x is 1.016234e-259 
  870. #&gt; x is 5.08117e-260 
  871. #&gt; x is 2.540585e-260 
  872. #&gt; x is 1.270293e-260 
  873. #&gt; x is 6.351463e-261 
  874. #&gt; x is 3.175732e-261 
  875. #&gt; x is 1.587866e-261 
  876. #&gt; x is 7.939329e-262 
  877. #&gt; x is 3.969664e-262 
  878. #&gt; x is 1.984832e-262 
  879. #&gt; x is 9.924161e-263 
  880. #&gt; x is 4.962081e-263 
  881. #&gt; x is 2.48104e-263 
  882. #&gt; x is 1.24052e-263 
  883. #&gt; x is 6.202601e-264 
  884. #&gt; x is 3.1013e-264 
  885. #&gt; x is 1.55065e-264 
  886. #&gt; x is 7.753251e-265 
  887. #&gt; x is 3.876625e-265 
  888. #&gt; x is 1.938313e-265 
  889. #&gt; x is 9.691564e-266 
  890. #&gt; x is 4.845782e-266 
  891. #&gt; x is 2.422891e-266 
  892. #&gt; x is 1.211445e-266 
  893. #&gt; x is 6.057227e-267 
  894. #&gt; x is 3.028614e-267 
  895. #&gt; x is 1.514307e-267 
  896. #&gt; x is 7.571534e-268 
  897. #&gt; x is 3.785767e-268 
  898. #&gt; x is 1.892883e-268 
  899. #&gt; x is 9.464417e-269 
  900. #&gt; x is 4.732209e-269 
  901. #&gt; x is 2.366104e-269 
  902. #&gt; x is 1.183052e-269 
  903. #&gt; x is 5.915261e-270 
  904. #&gt; x is 2.95763e-270 
  905. #&gt; x is 1.478815e-270 
  906. #&gt; x is 7.394076e-271 
  907. #&gt; x is 3.697038e-271 
  908. #&gt; x is 1.848519e-271 
  909. #&gt; x is 9.242595e-272 
  910. #&gt; x is 4.621298e-272 
  911. #&gt; x is 2.310649e-272 
  912. #&gt; x is 1.155324e-272 
  913. #&gt; x is 5.776622e-273 
  914. #&gt; x is 2.888311e-273 
  915. #&gt; x is 1.444156e-273 
  916. #&gt; x is 7.220778e-274 
  917. #&gt; x is 3.610389e-274 
  918. #&gt; x is 1.805194e-274 
  919. #&gt; x is 9.025972e-275 
  920. #&gt; x is 4.512986e-275 
  921. #&gt; x is 2.256493e-275 
  922. #&gt; x is 1.128246e-275 
  923. #&gt; x is 5.641232e-276 
  924. #&gt; x is 2.820616e-276 
  925. #&gt; x is 1.410308e-276 
  926. #&gt; x is 7.051541e-277 
  927. #&gt; x is 3.52577e-277 
  928. #&gt; x is 1.762885e-277 
  929. #&gt; x is 8.814426e-278 
  930. #&gt; x is 4.407213e-278 
  931. #&gt; x is 2.203606e-278 
  932. #&gt; x is 1.101803e-278 
  933. #&gt; x is 5.509016e-279 
  934. #&gt; x is 2.754508e-279 
  935. #&gt; x is 1.377254e-279 
  936. #&gt; x is 6.88627e-280 
  937. #&gt; x is 3.443135e-280 
  938. #&gt; x is 1.721568e-280 
  939. #&gt; x is 8.607838e-281 
  940. #&gt; x is 4.303919e-281 
  941. #&gt; x is 2.151959e-281 
  942. #&gt; x is 1.07598e-281 
  943. #&gt; x is 5.379898e-282 
  944. #&gt; x is 2.689949e-282 
  945. #&gt; x is 1.344975e-282 
  946. #&gt; x is 6.724873e-283 
  947. #&gt; x is 3.362437e-283 
  948. #&gt; x is 1.681218e-283 
  949. #&gt; x is 8.406091e-284 
  950. #&gt; x is 4.203046e-284 
  951. #&gt; x is 2.101523e-284 
  952. #&gt; x is 1.050761e-284 
  953. #&gt; x is 5.253807e-285 
  954. #&gt; x is 2.626904e-285 
  955. #&gt; x is 1.313452e-285 
  956. #&gt; x is 6.567259e-286 
  957. #&gt; x is 3.283629e-286 
  958. #&gt; x is 1.641815e-286 
  959. #&gt; x is 8.209074e-287 
  960. #&gt; x is 4.104537e-287 
  961. #&gt; x is 2.052268e-287 
  962. #&gt; x is 1.026134e-287 
  963. #&gt; x is 5.130671e-288 
  964. #&gt; x is 2.565336e-288 
  965. #&gt; x is 1.282668e-288 
  966. #&gt; x is 6.413339e-289 
  967. #&gt; x is 3.206669e-289 
  968. #&gt; x is 1.603335e-289 
  969. #&gt; x is 8.016673e-290 
  970. #&gt; x is 4.008337e-290 
  971. #&gt; x is 2.004168e-290 
  972. #&gt; x is 1.002084e-290 
  973. #&gt; x is 5.010421e-291 
  974. #&gt; x is 2.50521e-291 
  975. #&gt; x is 1.252605e-291 
  976. #&gt; x is 6.263026e-292 
  977. #&gt; x is 3.131513e-292 
  978. #&gt; x is 1.565757e-292 
  979. #&gt; x is 7.828783e-293 
  980. #&gt; x is 3.914391e-293 
  981. #&gt; x is 1.957196e-293 
  982. #&gt; x is 9.785978e-294 
  983. #&gt; x is 4.892989e-294 
  984. #&gt; x is 2.446495e-294 
  985. #&gt; x is 1.223247e-294 
  986. #&gt; x is 6.116236e-295 
  987. #&gt; x is 3.058118e-295 
  988. #&gt; x is 1.529059e-295 
  989. #&gt; x is 7.645296e-296 
  990. #&gt; x is 3.822648e-296 
  991. #&gt; x is 1.911324e-296 
  992. #&gt; x is 9.556619e-297 
  993. #&gt; x is 4.77831e-297 
  994. #&gt; x is 2.389155e-297 
  995. #&gt; x is 1.194577e-297 
  996. #&gt; x is 5.972887e-298 
  997. #&gt; x is 2.986444e-298 
  998. #&gt; x is 1.493222e-298 
  999. #&gt; x is 7.466109e-299 
  1000. #&gt; x is 3.733054e-299 
  1001. #&gt; x is 1.866527e-299 
  1002. #&gt; x is 9.332636e-300 
  1003. #&gt; x is 4.666318e-300 
  1004. #&gt; x is 2.333159e-300 
  1005. #&gt; x is 1.16658e-300 
  1006. #&gt; x is 5.832898e-301 
  1007. #&gt; x is 2.916449e-301 
  1008. #&gt; x is 1.458224e-301 
  1009. #&gt; x is 7.291122e-302 
  1010. #&gt; x is 3.645561e-302 
  1011. #&gt; x is 1.822781e-302 
  1012. #&gt; x is 9.113903e-303 
  1013. #&gt; x is 4.556951e-303 
  1014. #&gt; x is 2.278476e-303 
  1015. #&gt; x is 1.139238e-303 
  1016. #&gt; x is 5.696189e-304 
  1017. #&gt; x is 2.848095e-304 
  1018. #&gt; x is 1.424047e-304 
  1019. #&gt; x is 7.120236e-305 
  1020. #&gt; x is 3.560118e-305 
  1021. #&gt; x is 1.780059e-305 
  1022. #&gt; x is 8.900295e-306 
  1023. #&gt; x is 4.450148e-306 
  1024. #&gt; x is 2.225074e-306 
  1025. #&gt; x is 1.112537e-306 
  1026. #&gt; x is 5.562685e-307 
  1027. #&gt; x is 2.781342e-307 
  1028. #&gt; x is 1.390671e-307 
  1029. #&gt; x is 6.953356e-308 
  1030. #&gt; x is 3.476678e-308 
  1031. #&gt; x is 1.738339e-308 
  1032. #&gt; x is 8.691695e-309 
  1033. #&gt; x is 4.345847e-309 
  1034. #&gt; x is 2.172924e-309 
  1035. #&gt; x is 1.086462e-309 
  1036. #&gt; x is 5.432309e-310 
  1037. #&gt; x is 2.716155e-310 
  1038. #&gt; x is 1.358077e-310 
  1039. #&gt; x is 6.790387e-311 
  1040. #&gt; x is 3.395193e-311 
  1041. #&gt; x is 1.697597e-311 
  1042. #&gt; x is 8.487983e-312 
  1043. #&gt; x is 4.243992e-312 
  1044. #&gt; x is 2.121996e-312 
  1045. #&gt; x is 1.060998e-312 
  1046. #&gt; x is 5.304989e-313 
  1047. #&gt; x is 2.652495e-313 
  1048. #&gt; x is 1.326247e-313 
  1049. #&gt; x is 6.631237e-314 
  1050. #&gt; x is 3.315618e-314 
  1051. #&gt; x is 1.657809e-314 
  1052. #&gt; x is 8.289046e-315 
  1053. #&gt; x is 4.144523e-315 
  1054. #&gt; x is 2.072262e-315 
  1055. #&gt; x is 1.036131e-315 
  1056. #&gt; x is 5.180654e-316 
  1057. #&gt; x is 2.590327e-316 
  1058. #&gt; x is 1.295163e-316 
  1059. #&gt; x is 6.475817e-317 
  1060. #&gt; x is 3.237909e-317 
  1061. #&gt; x is 1.618954e-317 
  1062. #&gt; x is 8.094772e-318 
  1063. #&gt; x is 4.047386e-318 
  1064. #&gt; x is 2.023693e-318 
  1065. #&gt; x is 1.011846e-318 
  1066. #&gt; x is 5.059232e-319 
  1067. #&gt; x is 2.529616e-319 
  1068. #&gt; x is 1.264808e-319 
  1069. #&gt; x is 6.32404e-320 
  1070. #&gt; x is 3.16202e-320 
  1071. #&gt; x is 1.58101e-320 
  1072. #&gt; x is 7.90505e-321 
  1073. #&gt; x is 3.952525e-321 
  1074. #&gt; x is 1.976263e-321 
  1075. #&gt; x is 9.881313e-322 
  1076. #&gt; x is 4.940656e-322 
  1077. #&gt; x is 2.470328e-322 
  1078. #&gt; x is 1.235164e-322 
  1079. #&gt; x is 5.928788e-323 
  1080. #&gt; x is 2.964394e-323 
  1081. #&gt; x is 1.482197e-323 
  1082. #&gt; x is 9.881313e-324 
  1083. #&gt; x is 4.940656e-324 
  1084. #&gt; x is 0

<sup>Created on 2023-03-06 with reprex v2.0.2</sup>

huangapple
  • 本文由 发表于 2023年3月7日 03:05:20
  • 转载请务必保留本文链接：https://go.coder-hub.com/75654832.html
  • bisection
  • r
  • recursion
  • while-loop
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